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A369250
Primes for which there is at least one representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.
4
71, 103, 131, 151, 167, 191, 199, 211, 239, 251, 263, 271, 311, 331, 359, 383, 419, 431, 439, 467, 479, 487, 491, 503, 563, 587, 599, 607, 631, 647, 691, 719, 727, 739, 743, 751, 811, 823, 839, 859, 863, 887, 911, 919, 971, 983, 991, 1019, 1031, 1051, 1063, 1091, 1103, 1151, 1163, 1187, 1223, 1231, 1279, 1283, 1291
OFFSET
1,1
COMMENTS
All such primes are by necessity of the form 4m+3 (in A002145). See A369249 for those 4m+3 primes that do not have such a representation.
Also by necessity, in these cases the primes in the sum (p*q + p*r + q*r) must all be distinct, that is, we actually need p < q < r, otherwise the sum would not be a prime.
LINKS
EXAMPLE
71 is present as 71 = (3*5) + (3*7) + (5*7) = A003415(105).
PROG
(PARI) isA369250(n) = (isprime(n) && (A369054(n)>0)); \\ Needs also program from A369054.
CROSSREFS
Primes in A369251.
Setwise difference A002145 \ A369249.
Subsequence of A189441.
Sequence in context: A339466 A339463 A166576 * A195270 A142111 A164289
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 22 2024
STATUS
approved